A Clairaut equation is a first-order equation of the form A remarkable feature of this nonlinear equation is that its general solution has a very simple form. This is an ...

A linear second-order ordinary differential equation is said to be exact if An exact linear second-order ODE is solved by reduction to a linear first-order ODE.

Solving linear first-order ODEs is straightforward and only requires the use of a suitable integrating factor. In sharp contrast, there are a large number of methods ...

Systems of ODEs are important in various fields of science, such as the study of electricity and population biology. Like single ODEs, systems of ODEs can classified as ...

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...

An Euler equation has the general form Euler equations can be solved by transforming them to equations with constant coefficients. This is an example of an Euler equation.

Introduction to Dynamic Advanced Dynamic Functionality

Mathematica notebooks provide a sophisticated environment for creating technical documents. But particularly if you want to merge your work with existing material in TeX, you ...

In the standard notebook front end, Mathematica allows you to set a large number of global options. The values of all these options are by default saved in a "preferences ...

The Basic Constructs Classes of Functionality Options Syntax